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Abstract

The optical thermodynamic efficiency is a comprehensive metric that takes into account all loss mechanisms associated with transferring flux from the source to the target phase space, which may include losses due to inadequate design, non-ideal materials, fabrication errors, and less than maximal concentration. We discuss consequences of Fermat’s principle of geometrical optics and review étendue dilution and optical loss mechanisms associated with nonimaging concentrators. We develop an expression for the optical thermodynamic efficiency which combines the first and second laws of thermodynamics. As such, this metric is a gold standard for evaluating the performance of nonimaging concentrators. We provide examples illustrating the use of this new metric for concentrating photovoltaic systems for solar power applications, and in particular show how skewness mismatch limits the attainable optical thermodynamic efficiency.

Boundaries of direction-cosine regions corresponding to source (red line) and target (blue line) for second example. The unit circle is depicted as a dashed black line. The daily operation time is T = 6 hr and the maximum allowed incidence angle on the target is θtrg = 60°.

Source and target translational skewness distributions for the second example. The source has unit area and the target étendue equals that of the source. The daily operation time is T = 6 hr and the maximum allowed incidence angle on the target is θtrg = 60°.

Source and target translational skewness distributions for the second example. The source has unit area and the target area has been adjusted to the smallest value that allows the target’s skewness distribution to completely enclose the source’s skewness distribution. The daily operation time is T = 6 hr and the maximum allowed incidence angle on the target is θtrg = 60°.